Parameter Identification in Nonlinear Solid Mechanics

LecturerDr.-Ing. Martin Abendroth
AudienceDiploma and master courses
Volume2/1/0 SWS (lecture/exercise/practical course)
InstructorsDr.-Ing. Martin Abendroth


The organization of the course can be found on OPAL under Parameter Identification in Nonlinear Solid Mechanics. There you find all materials, which are necessary to complete tasks for the exercises as well as. The materials will be provided prior to the lectures and exercises.


The calibration of parameters plays a central role in establishing predictively accurate constitutive models for complex, nonlinear material responses. In numerical optimization-based approaches to parameter identification, an objective function that measures deviations between simulation results and experimental data is minimized to compute optimal parameter sets.

After motivating the inverse problem of parameter identification the course provides an introduction to fundamental theoretical and algorithmic concepts of (constrained) nonlinear optimization. The lectures are accompanied by programming exercises that lead to hands-on experience with implementing and testing such optimization methods.

In the second part of the course, students learn to apply these numerical tools to the specific problem of parameter identification for nonlinear (elasto-plastic, visco-elastic etc.) material models. To obtain the necessary experimental data, students will help conduct experiments in the materials characterization laboratory of the solid mechanics group.

The lectures will further address advanced concepts, such as parameter identification via inhomogeneous deformation processes by combining digital image correlation and finite element analysis. Lastly, it is demonstrated that very similar numerical concepts can be employed in solving structural optimization problems of nonlinear solid mechanics.


  • Introduction
  • Unconstrained nonlinear optimization
    • Gradient-free methods
    • Gradient-based methods
    • Evolution strategy based methods
  • Constrained nonlinear optimization
    • Active-set strategy
    • Penalty method
    • Fischer-Burmeister complementary function approach
  • Parameter identification for homogenous deformation states
    • 1D plasticity
  • Parameter identification for inhomogenous deformation states
    • Finite Element Method and Digital Image Correlation
    • Scipy libraries minimize and least squares
    • Parameter identification from small punch tests
    • Parameter identification from tensile tests on notched bars


  • Introduction
  • Steepest descent
  • Conjugate gradients
  • Penalty method
  • Active set strategy
  • 1D plasticity
  • Finite element method
  • Digital image correlation


  • J. Nocedal and S. J. Wright, Numerical Optimization, Springer-
    Verlag, Berlin, 2nd edition, 2006.
  • D. P. Bertsekas, Nonlinear Programming, Athena Scientific,
    Belmont, MA, 2nd edition, 1999.
  • D. G. Luenberger, Linear and Nonlinear Programming, Addison-
    Wesley, Reading, MA, 2nd edition, 1984.
  • R. Mahnken, Identification of Material Parameters for Constitutive
    Equations, In Encyclopedia of Computational Mechanics, chapter
    19, pages 637-655. John Wiley & Sons, New York, 2004.

Schedule for winter term 2021/2022

Lectures: Friday, 07:30 - 09:00, Room: FOR-0221 or Online: OPAL
Exercises group 1: Monday, uneven weeks, 14:00-15:30, Room: WEI-1218a or Online: OPAL
Exercises group 2: Tuesday, even weeks, 11:30-13:00, Room: WEI-1218a or Online: OPAL

*First lecture: Friday, 29.10.2021, 07:30 - 09:00, Room: FOR-0221 or Online: OPAL
*First exercise group 1: Monday, 25.10.2021, Tuesday, 14:00-15:30, Room: WEI-1218a or Online: OPAL
*First exercise group 2: Tuesday,02.11.2021, Tuesday, 11:30-13:00, Room: WEI-1218a or Online: OPAL